A need exists for an emitter, e.g., a resonator, capable of resonating at multiple predefined frequencies, simultaneously having significant signal magnification capacities, increased strength, reduced weight, reduced cost, smaller form factor, elimination of need to change resonator plates to change frequencies, reduced signal reproduction degradation, and an ability to manufacture using desirable manufacturing processes and equipment. One aspect of the invention relates to a method of using fractal shapes to allow for multiple resonances in a single metallic plate for use with wavelet transforms filtered in a wavelet domain to produce or reproduce a complex waveform over a wide frequency range. Presently acoustic resonators do not exist that can, for example, resonate with a single plate, at multiple frequencies, at precise intervals such as octaves.
For example, with fractals, a prescribed magnification factor can be realized in a fractal pattern in accordance with various embodiments of the invention. Since a resonance frequency of a thin metallic circular plate is inversely proportional to a square of the diameter of the circular plate, a fractal pattern such as shown below appears to have multiple diameters, with each smaller repeated image in the fractal being reduced in size by the magnification factor of the fractal. If the magnification factor is set to the square root of two, then each successive smaller imager in the fractal will resonate at twice the frequency of the preceding larger image.
According to an illustrative embodiment of the present disclosure, exemplary fractal patterns created in accordance with an embodiment of the invention can provide multiple acoustic resonances proportional to a magnification factor of a fractal. A variety of experiments demonstrated that there is significant difficulty in producing an embodiment adapted to produce results or effects associated with the invention showing that merely attempting to use a fractal design with wavelet systems did not easily result in an operable embodiment. For example, FIG. 1 shows an eight vertex fractal with the magnification factor set to the point just before overlap of the fractal images. However, this fractal could not be manufactured to create an operable result that could retain structural integrity. For example, an effort to create an embodiment using a laser to burn a hole in a thin metal disk at each point in the fractal resulted in a resulting structure that could not maintain structural integrity or reproduce a resonance signal without substantial degradation.
According to a further illustrative embodiment of the present disclosure, exemplary fractal patterns provide multiple acoustic resonances proportional to the magnification factor of the fractal. For example, FIG. 2 shows a seven vertex fractal with the magnification factor set to leave some metal between successive images of the fractal pattern.
Additional features and advantages of the present invention will become apparent to those skilled in the art upon consideration of the following detailed description of the illustrative embodiment exemplifying the best mode of carrying out the invention as presently perceived.